WO2020010602A1 - Procédé et système de reconnaissance et de construction faciales basés sur une décomposition de matrice non-négative non linéaire, et support d'informations - Google Patents

Procédé et système de reconnaissance et de construction faciales basés sur une décomposition de matrice non-négative non linéaire, et support d'informations Download PDF

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WO2020010602A1
WO2020010602A1 PCT/CN2018/095554 CN2018095554W WO2020010602A1 WO 2020010602 A1 WO2020010602 A1 WO 2020010602A1 CN 2018095554 W CN2018095554 W CN 2018095554W WO 2020010602 A1 WO2020010602 A1 WO 2020010602A1
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matrix
negative
function
kernel
face recognition
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PCT/CN2018/095554
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Chinese (zh)
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陈文胜
刘敬敏
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深圳大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition

Definitions

  • the present invention relates to the technical field of data processing, and in particular, to a method, system, and storage medium for constructing face recognition based on non-linear non-negative matrix factorization.
  • biometric technology that uses the inherent physiological and behavioral characteristics of the human body for personal identification has become one of the most active research fields.
  • face recognition is non-invasive, non-mandatory, non-contact And concurrency.
  • Face recognition technology includes two stages.
  • the first stage is feature extraction, that is, the extraction of facial feature information in the face image. This stage directly determines the quality of face recognition technology.
  • the second stage is identification. Personal identification is performed based on the extracted feature information.
  • Principal component analysis (PCA) and singular value decomposition (SVD) are more classic feature extraction methods, but the feature vectors proposed by these two methods usually contain negative elements, so these methods do not have the original sample with non-negative data. Rationality and interpretability.
  • Non-negative matrix factorization is a feature extraction method for processing non-negative data. It is widely used in applications such as hyperspectral data processing and face image recognition.
  • the NMF algorithm has non-negative restrictions on the extracted features during the non-negative data matrix decomposition of the original sample, that is, all components after the decomposition are non-negative, so non-negative sparse features can be extracted.
  • the essence of the NMF algorithm is to approximately decompose the non-negative matrix X into the product of the base image matrix W and the coefficient matrix H, that is, X ⁇ WH, and W and H are both non-negative matrices.
  • each column of the matrix X can be represented as a non-negative linear combination of the matrix W column vectors, which also conforms to the construction basis of the NMF algorithm-the perception of the whole is composed of the perception of the parts that make up the whole (pure additive) .
  • NMF local NMF algorithm
  • DNMF discriminative NMF algorithm
  • SNMF symmetric NMF algorithm
  • the kernel method is an effective method. It extends the linear algorithm to a non-linear algorithm and provides a beautiful theoretical framework.
  • the basic idea of the kernel method is to use a non-linear mapping function to map the original data into a high-dimensional feature space, so that the mapped data is linearly separable, and then apply a linear algorithm to the mapped data.
  • the kernel method the most critical part is the use of kernel techniques. By using the kernel function to replace the inner product of the mapped data, there is no need to know the specific analytical formula of the non-linear mapping function.
  • the use of nuclear techniques reduces the difficulty of extending the mapping to the functional space, the regenerating nuclear Hilbert space (RKHS).
  • NMF nonlinear NMF algorithm
  • NLNMF algorithms include polynomial kernel non-negative matrix factorization (PNMF) and Gaussian kernel non-negative matrix factorization (RBFNMF), and their loss functions are constructed based on the square of the F-norm.
  • PNMF polynomial kernel non-negative matrix factorization
  • RBFNMF Gaussian kernel non-negative matrix factorization
  • ⁇ x 1 , x 2 , ..., x n ⁇ be a set of data in the original sample space.
  • the main idea of the kernel method is to map the samples from the original space to a higher-dimensional feature space through a non-linear mapping function ⁇ ( ⁇ ), so that the samples are linearly separable in this feature space, and as long as the original space is finite-dimensional , Then there must be such a high-dimensional feature space.
  • ⁇ non-linear mapping function
  • the inner product of x i and x j in the feature space can be calculated by using their function k ( ⁇ , ⁇ ) in the original sample space. This not only solves these problems, but also simplifies the calculation process.
  • NLNMF The main purpose of NLNMF is to use kernel methods to solve the application of NMF in nonlinear problems.
  • the NMF algorithm is used to process the mapped data in the high-dimensional feature space, and ⁇ (X) is approximately decomposed into the product of two matrices ⁇ (W) and H, that
  • the kernel function k ( ⁇ , ⁇ ) implicitly defines a high-dimensional feature space. If the kernel function is not selected properly, it means that the sample data is mapped to an inappropriate feature Space is likely to cause poor performance.
  • Another major factor is the construction of the loss function F (W, H).
  • the loss function determines the accuracy of the NLNMF algorithm to a certain extent. Different loss functions have different emphasis, and not all loss functions can be used in the feature space. Therefore, the selection of the loss function is also important.
  • the commonly used loss function is F F (W, H) constructed according to the F-norm, that is,
  • Nonlinear non-negative matrix factorization algorithm PNMF based on polynomial kernel
  • the loss function of the polynomial kernel non-negative matrix factorization algorithm is F F (W, H). It solves the optimization problem (1) based on the polynomial kernel function.
  • the updated iterative formulas for W and H are:
  • ⁇ is a diagonal matrix whose diagonal elements are
  • the loss functions of current non-linear non-negative matrix factorization algorithms are all based on the F-norm.
  • the F-norm has two major shortcomings, namely its sensitivity to outliers and poor sparsity. This makes the algorithm Has poor stability and cannot well resist changes in pose and illumination in face recognition;
  • the power exponent of the polynomial kernel function in polynomial kernel non-negative matrix factorization (PNMF) can only be an integer, when the power exponent is a fraction There is no guarantee that it is still a kernel function, and the discriminative ability of the kernel function is weakened when the power exponent is an integer.
  • the invention provides a method for constructing face recognition based on nonlinear non-negative matrix factorization, which includes the following steps:
  • Loss characterization step use the l 2, p -norm of the matrix to characterize the loss degree after matrix decomposition;
  • Sparsity enhancement step Use the l 1 -norm of the matrix to enhance the sparse representation of features, and add a regular term about the matrix H to the loss function;
  • Steps to obtain the updated iterative formula for the non-negative matrix factorization of the fractional power inner product kernel Use the fractional power inner product kernel function to form the optimization problem to be solved. Solve H by using the gradient descent method and W by the exponential gradient descent method, so that An updated iterative formula for the fractional power inner product kernel non-negative matrix factorization is obtained.
  • the construction method further includes a convergence verification step.
  • the convergence verification step the convergence of the algorithm is proved by constructing an auxiliary function.
  • the updated iterative formula of the fractional power inner product kernel non-negative matrix factorization is:
  • the non-negative non-negative matrix factorization face recognition method provided by the present invention further includes a training step.
  • the training step includes:
  • the first step transform the training sample image into a training sample matrix X, set an error threshold ⁇ , a maximum number of iterations I max , and initialize the base image matrix W and the coefficient matrix H;
  • the second step update the iteration formula of the non-negative matrix factorization of the inner product kernel of fractional powers to update W and H;
  • the non-linear non-negative matrix factorization face recognition method further includes performing a testing step after the training step, the testing step includes:
  • Step Six If Then the sample y is classified into the l class.
  • the updated iteration formula of the non-negative matrix factorization of the fractional power inner product kernel in the training step is:
  • the present invention also provides a non-linear non-negative matrix factorization face recognition system, which includes a memory, a processor, and a computer program stored on the memory.
  • the computer program is configured to implement all functions when called by the processor. The steps of the method are described.
  • the invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program configured to implement the steps of the method when called by a processor.
  • the beneficial effects of the present invention are: 1. By using 1, 2, p -norm instead of F-norm to measure the loss of matrix factorization, the problem of singular value sensitivity in the existing kernel non-negative matrix factorization algorithm is solved, and the enhancement The stability of the kernel non-negative matrix factorization algorithm proposed by the present invention; 2. The sparseness of the feature representation of the algorithm of the present invention is enhanced by adding a regularization restriction on the coefficient matrix H to the objective function; 3.
  • the kernel non-negative matrix factorization with a new objective function is integrated with the fractional power inner product kernel function to obtain a sparse fractional inner product nonlinear non-negative matrix factorization algorithm with efficient recognition performance, which solves the hyperparameters of the polynomial kernel function Problems that can only be integers improve the discriminative ability of the algorithm.
  • FIG. 1 is a flowchart of an algorithm construction process of the present invention
  • FIG. 3 is a comparison diagram of the recognition rate of the proposed algorithm and related algorithms (KLPP, LNMF, PNMF) on the CMU PIE face database;
  • FIG. 4 is a convergence curve diagram of the algorithm of the present invention.
  • the present invention discloses a method for constructing non-linear non-negative matrix factorization face recognition, and specifically discloses a method for constructing non-linear non-negative matrix factorization face recognition based on l 2, p modules. .
  • the method for constructing non-linear non-negative matrix factorization face recognition includes the following steps:
  • Loss characterization step use the l 2, p -norm of the matrix to characterize the loss degree after matrix decomposition;
  • Sparsity enhancement step Use the l 1 -norm of the matrix to enhance the sparse representation of features, and add a regular term about the matrix H to the loss function;
  • Steps to obtain the updated iterative formula for the non-negative matrix factorization of the fractional power inner product kernel Use the fractional power inner product kernel function to form the optimization problem to be solved. Solve H by using the gradient descent method and W by the exponential gradient descent method, An updated iterative formula for the fractional power inner product kernel non-negative matrix factorization is obtained.
  • the construction method also includes a convergence verification step.
  • the convergence verification step the convergence of the algorithm is proved by constructing an auxiliary function.
  • the present invention discloses a non-linear non-negative matrix factorization face recognition method, which includes a training step.
  • the training step includes:
  • the first step transform the training sample image into a training sample matrix X, set an error threshold ⁇ , a maximum number of iterations I max , and initialize the base image matrix W and the coefficient matrix H;
  • the second step update the iteration formula of the non-negative matrix factorization of the inner product kernel of fractional powers to update W and H;
  • the nonlinear non-negative matrix factorization face recognition method further includes performing a testing step after the training step.
  • the testing step includes:
  • Step Six If Then the sample y is classified into the l class.
  • the updated iterative formula of the non-negative matrix factorization of the fractional power inner product kernel in the training step of the non-linear non-negative matrix factorization face recognition method is:
  • the invention also discloses a non-linear non-negative matrix factorization face recognition system, which includes: a memory, a processor, and a computer program stored on the memory.
  • the computer program is configured to implement all functions when called by the processor. The steps of the method are described.
  • the invention also discloses a computer-readable storage medium.
  • the computer-readable storage medium stores a computer program configured to implement the steps of the method when called by a processor.
  • Keyword interpretation (note: roughly explain the concepts of some key words related to the present invention)
  • l 2 p -norm contains F-norm.
  • NMF Non-negative Matrix Factorization
  • the base image matrix and the coefficient matrix, respectively.
  • the loss function is defined based on the F-norm, as:
  • ⁇ be the input space
  • k ( ⁇ , ⁇ ) be a symmetric function defined on ⁇ ⁇ ⁇
  • the kernel matrix K is always positive semidefinite:
  • the present invention introduces a fractional power inner product kernel function. Assume Is an m-dimensional column vector, and is defined in the present invention d> 0.
  • Theorem 1 For arbitrary vectors And positive real numbers The function k is defined as:
  • k is a kernel function. We call this function a fractional power inner product kernel function.
  • the present invention uses l 2, p -norm (0 ⁇ p ⁇ 2) to characterize the loss function, that is:
  • ⁇ 0 is a regular term parameter
  • problem (2) also evolved into two sub-problems, namely:
  • the gradient descent method is used to solve the coefficient matrix H, which includes:
  • the selection step vector is:
  • This updated iterative formula can be transformed into a matrix form with the following theorem.
  • Theorem 2 Fixed matrix W.
  • the objective function f 1 (H) is non-increasing.
  • the coefficient matrix H in subproblem (3) is updated in the following iterative manner:
  • Non-linear generalized exponential gradient descent methods using gradient descent methods are:
  • the selection step size is:
  • Extending it to the matrix form can get the updated iterative formula of W, such as the following theorem.
  • Theorem 3 The fixed matrix H, the objective function f 2 (H) is non-increasing.
  • the base image matrix W in the subproblem (4) is updated in the following iterative manner:
  • Definition 1 For any matrices H and H (t) , if the conditions are met
  • G (H, H (t) ) is called an auxiliary function of function f (H).
  • Theorem 4 Is a diagonal matrix with diagonal elements as Then
  • G 1 (H, H (t) ) is the auxiliary function of f 1 (H), which is proved.
  • Theorem 5 Let Is a symmetric matrix with elements
  • ⁇ maps it into the feature space
  • ⁇ (y) can be expressed as a linear combination of the column vectors of the mapped base image matrix ⁇ (W) as
  • the beneficial effects of the present invention are: 1. By using 1, 2, p -norm instead of F-norm to measure the loss of matrix factorization, the problem of singular value sensitivity in the existing kernel non-negative matrix factorization algorithm is solved, and the enhancement The stability of the kernel non-negative matrix factorization algorithm proposed by the present invention; 2. The sparseness of the feature representation of the algorithm of the present invention is enhanced by adding a regularization restriction on the coefficient matrix H to the objective function; 3.
  • the kernel non-negative matrix factorization with a new objective function is integrated with the fractional power inner product kernel function to obtain a sparse fractional inner product nonlinear non-negative matrix factorization algorithm with efficient recognition performance, which solves the hyperparameters of the polynomial kernel function Problems that can only be integers improve the discriminative ability of the algorithm.

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Abstract

L'invention concerne un procédé et un système de reconnaissance et de construction faciales basés sur une décomposition de matrice non-négative non linéaire, ainsi qu'un support d'informations. Le procédé comprend les étapes consistant : à représenter le degré de perte après décomposition de matrice à l'aide d'une norme l 2,p-norm ; à améliorer la représentation de dispersion d'une caractéristique en utilisant la norme l 1-norm d'une matrice, et à ajouter un terme de régularisation concernant une matrice H dans une fonction de perte ; à construire une fonction cible F(W,H) au moyen d'un degré d'étape de représentation de perte et d'une étape d'amélioration de la dispersion ; et à obtenir une formule d'itération de mise à jour pour la décomposition de matrice non négative de noyau du produit interne de puissance fractionnaire. Le procédé peut résoudre le problème selon lequel un algorithme de décomposition de matrice non négative de noyau est sensible à une valeur singulière, peut améliorer la dispersion de l'algorithme en une représentation de caractéristiques, et résout également le problème selon lequel des super-paramètres d'une fonction de noyau polynomial peuvent uniquement être des nombres entiers.
PCT/CN2018/095554 2018-07-13 2018-07-13 Procédé et système de reconnaissance et de construction faciales basés sur une décomposition de matrice non-négative non linéaire, et support d'informations WO2020010602A1 (fr)

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CN112116017A (zh) * 2020-09-25 2020-12-22 西安电子科技大学 基于核保持的数据降维方法
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CN112966735A (zh) * 2020-11-20 2021-06-15 扬州大学 一种基于谱重建的监督多集相关特征融合方法
CN113705674A (zh) * 2021-08-27 2021-11-26 西安交通大学 一种非负矩阵分解聚类方法、装置及可读存储介质
CN114936597A (zh) * 2022-05-20 2022-08-23 电子科技大学 一种局部信息增强子空间真假目标特征提取方法
CN116189760A (zh) * 2023-04-19 2023-05-30 中国人民解放军总医院 基于矩阵补全的抗病毒药物筛选方法、系统及存储介质

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CN111967499A (zh) * 2020-07-21 2020-11-20 电子科技大学 基于自步学习的数据降维方法
CN111967499B (zh) * 2020-07-21 2023-04-07 电子科技大学 基于自步学习的数据降维方法
CN112116017A (zh) * 2020-09-25 2020-12-22 西安电子科技大学 基于核保持的数据降维方法
CN112116017B (zh) * 2020-09-25 2024-02-13 西安电子科技大学 基于核保持的图像数据降维方法
CN112966735B (zh) * 2020-11-20 2023-09-12 扬州大学 一种基于谱重建的监督多集相关特征融合方法
CN112966735A (zh) * 2020-11-20 2021-06-15 扬州大学 一种基于谱重建的监督多集相关特征融合方法
CN112598130A (zh) * 2020-12-09 2021-04-02 华东交通大学 基于自编码器和奇异值阈值的土壤湿度数据重构方法和计算机可读存储介质
CN112598130B (zh) * 2020-12-09 2024-04-09 华东交通大学 基于自编码器和奇异值阈值的土壤湿度数据重构方法和计算机可读存储介质
CN113705674A (zh) * 2021-08-27 2021-11-26 西安交通大学 一种非负矩阵分解聚类方法、装置及可读存储介质
CN113705674B (zh) * 2021-08-27 2024-04-05 西安交通大学 一种非负矩阵分解聚类方法、装置及可读存储介质
CN114936597B (zh) * 2022-05-20 2023-04-07 电子科技大学 一种局部信息增强子空间真假目标特征提取方法
CN114936597A (zh) * 2022-05-20 2022-08-23 电子科技大学 一种局部信息增强子空间真假目标特征提取方法
CN116189760B (zh) * 2023-04-19 2023-07-07 中国人民解放军总医院 基于矩阵补全的抗病毒药物筛选方法、系统及存储介质
CN116189760A (zh) * 2023-04-19 2023-05-30 中国人民解放军总医院 基于矩阵补全的抗病毒药物筛选方法、系统及存储介质

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